"We may – paraphrasing the famous sentence of George Orwell – say that
'all mathematics is beautiful, yet some is more beautiful than the other'.
But the most beautiful in all mathematics is the zeta function. There is no
doubt about it."

"...a variety of evidence suggests that underlying Riemann's zeta
function is some unknown classical, mechanical system whose trajectories
are chaotic and without [time-reversal] symmetry, with the property that,
when quantised, its allowed energies are the
Riemann zeros. These connections between the
seemingly disparate worlds of quantum mechanics and number theory are
tantalising."

Critical Strip Explorer v0.67, a wonderful applet produced by Raymond Manzoni
for this site – explore the behaviour of the Riemann zeta function in
and around the critical strip in a highly visual, interactive way. The
resulting images are quite astonishing!

more applets for exploring the behaviour of the Riemann zeta function can be found on Glen Pugh's homepage, as well as here.